The Electromagnetic Decays of $B^{\pm}_c(2S)$

TL;DR

This paper calculates the electromagnetic decay widths of the recently observed $B_c(2S)$ meson using the Bethe-Salpeter method, providing specific decay width values and including relativistic corrections.

Contribution

It presents the first detailed calculation of $B_c(2S)$ electromagnetic decay widths using an instantaneous Bethe-Salpeter approach with relativistic effects.

Findings

Calculated decay widths: 0.192 keV, 2.24 keV, and 11.4 keV for different channels.

Provides wave functions for P-wave $B_c$ mesons with mixing of states.

Includes relativistic corrections in decay amplitude calculations.

Abstract

We calculate the electromagnetic (EM) decay widths of the $B^{\pm}_c(2S)$ meson, which is observed recently by the ATLAS Collaboration. The main EM decay channels of this particle are $1{^3S_1}\gamma$ and $1{P}\gamma$, which, in literature, are estimated to have the branching ratio of about $1/10$. In this work, we get the partial decay widths: $\Gamma(2{^1S_0}\rightarrow 1{^3S_1}\gamma)=0.192$ keV, $\Gamma(2{^1S_0}\rightarrow 1{P_1}\gamma) = 2.24$ keV and $\Gamma(2{^1S_0}\rightarrow 1{P_1^\prime}\gamma) = 11.4$ keV. In the calculation, the instantaneous approximated Bethe-Salpeter method is used. For the $P$-wave $B_c$ mesons, the wave functions are given by mixing the $^3P_1$ and $^1P_1$ states. Within the Mandelstam formalism, the decay amplitude is given, which includes the relativistic corrections.